Multilayer Reconstruction and Order-Disorder Structural Phase Transition of the Clean W(001) Surface.

The clean W(001) surface is known to undergo a phase transition, reversible with temperature, between (1 times 1) and (sqrt {2} times sqrt{2})R45 ^circ periodic structures. The currently accepted model of the reconstructed structure in the low temperature phase consists of laterally displaced top-layer atoms. The nature of the phase transition, however, is not so widely agreed upon. In the present work, surface x-ray diffraction has been used in addition to LEED to study the structure and phase transition of the clean W(001) surface. The great advantage of x-ray diffraction over LEED is that the intensity of scattered radiation can be straightforwardly analyzed with kinematical theory. In the case of the reconstructed surface, extra fractional-order reciprocal lattice rods are present far away from the bulk Bragg peaks so that the surface diffracted intensity can be specifically studied. Contrary to the prediction of the current model of the reconstructed surface, rotating anode based measurements show that the integrated intensity along the rods is modulated with a periodicity of the inverse of the layer spacing ( {a_{o}over 2} = 1.58A). This behavior is well explained by including atomic displacements in the second layer in the same fashion as the top layer. The best-fit structural parameters are Delta_1 = 0.24 +/- 0.025A, Delta_2 = 0.046 +/- 0.016A, and d_ {12} = 1.52 +/- 0.16A which are the top layer and second layer displacements and the interlayer spacing, respectively. Inclusion of second layer displacements is important for resolving discrepancies between theory and experiment. Synchrotron based measurements of the surface reconstruction of clean W(001) through its phase transition at about 230K reveals that the superlattice diffraction peak intensity decreases by a factor of 1000 over the temperature range studied. However, the integrated intensity is nearly conserved by the compensating broadening of the peak widths. This indicates that the surface undergoes an order-disorder transition with little change in the magnitude of atomic displacements. No shift of the superlattice diffraction peak position is seen at elevated temperatures in contradiction to Helium atom diffraction results. The critical behavior is also compared with the predictions of the 2D XY and Ising models.